A differentiable EFIE–MoM framework for surface-impedance inverse design of reactive metasurfaces
Description
We present DiffMoM.jl, an open-source Julia package for differentiable electric-field integral-equation (EFIE) method-of-moments (MoM) analysis and surface-impedance inverse design of single-layer reactive metasurfaces with Rao–Wilton–Glisson (RWG) basis functions. The implementation exposes a reproducible forward–adjoint pipeline in which impedance sensitivities are assembled analytically and scalar radiation objectives are differentiated without differentiating through the linear solver. Quadratic objectives require one adjoint solve, directivity-ratio objectives require two, and full central finite-difference gradients require \(O(P)\) additional forward solves for \(P\) design parameters. Verification combines energy-balance checks, mesh-sweep adjoint/finite-difference agreement, and an independent Bempp-cl comparison. Across the tested meshes, the energy-balance error remains within 2%, the mesh-sweep gradient error remains below 6 x 10^-5, and beam-centric Bempp-cl agreement stays within 0.38 dB on main-beam level and 0.47 dB on sidelobe suppression across seven reactive cases. A 4λ x 4λ, 144-cell beam-steering benchmark raises the target-angle gain by about 23 dB relative to a perfect electric conductor within the stated dense-solver scope.